Abstract. We aim to reconcile the recently published, apparently contrasting results
regarding the relative importance of tropical upwelling versus horizontal
transport for the seasonality of ozone above the tropical tropopause.
Different analysis methods in the literature (Lagrangian versus Eulerian,
and isentropic versus pressure vertical coordinates) yield different
perspectives of ozone transport, and the results must be carefully compared
in equivalent terms to avoid misinterpretation. By examining the Lagrangian
calculations in the Eulerian formulation, we show here that the results are
in fact consistent with each other and with a common understanding of the
ozone transport processes near and above the tropical tropopause.

We further emphasize that the complementary approaches are suited for
answering two different scientific questions: (1) what drives the observed
seasonal cycle in ozone at a particular level above the tropical tropopause?
and (2) how important is horizontal transport from mid-latitudes for ozone
concentrations in the tropical lower stratosphere? Regarding the first
question, the analysis of the transformed Eulerian mean (TEM) ozone budget
shows that the annual cycle in tropical upwelling is the main forcing of the
ozone seasonality at altitudes with large vertical gradients in the tropical
lower stratosphere. To answer the second question a Lagrangian framework must
be used, and the results show that a large fraction (~50%) of the
ozone molecules ascending through the tropical lower stratosphere is of
extra-tropical origin and has been in-mixed from mid-latitudes.